I started out with a noname BD-130 type airbrush and a compressor made from a fridge compressor and an old camping gas tank. If you type BD130 airbrush into ebay you'll find loads, it's really a cheapo Chinese one. It's not great but I painted quite a few models successfully with it including pre-shading, highlighting. Maybe I was just lucky?
A lot rides on how much you maintain and clean it. Take a lot of time on understanding how to take it apart, put it back together, how to clean it and make sure you clean it properly every time. I don't know about other types but the Achilles-heel of my cheapo airbrushes were the nozzle seals. They died after 2-3 cleanings and when that happens the brush will spray in a pulsating way, like a machine gun instead of a steady stream. If that happens you need to replace the nozzle seal. Either get some genuine seals or you can do what I did and kept a few of those rubber inserts from a beer cap and cut out small seals from the thicker edge. I would say a compressor with air tank is a must.
That being said, I recently replaced it with a Harder&Steenbeck and what a difference...